Sample Problems for Exam 2
Math 365

1. Here is a set of numbers.

   

   1. Compute the mean.
   2. Compute the median.
   3. Compute the Standard Deviation
2. Describe the difference between a ``population'' and a ``sample.''
3. What does it mean to say that a sample is random?
4. If you want to make inferences based on a sample, is it important that your sample be random? If so, why?
5. Suppose someone tells you that the average age at which people begin to drink alcohol is 19 years old and that since this is the case we could lower the drinking age to 19 without effecting the average age at which people begin to drink. Is this argument a valid statistical argument? (I don't care what your position is on the drinking age, I want to know if the given argument is statisticly valid.)
6. How many ways are there to roll a sum of 6 on a pair of six-sided dice? How many ways are there to roll a sum of 6 on a pair of 10 sided dice?
7. How many seven digit phone numbers exist if the first digit may not be a zero?
8. How many ways are there to form a committe of six people from a class of one hundred people if
   1. there are no restrictions
   2. there must be three men and three women on the committee? (there are 45 men and 55 women in the class.)
   3. Mary must be on the committee?
9. Define what an experiment is and give an example of an experiment.
10. What is a sample space? Give an example of an experiment and the sample space this experiment will generate.
11. What does it mean for a sample space to have equally likely outcomes? How do you assign theoretical probability? How do you assign empirical probability?
12. If a jar has 12 red, 3 blue and 6 white balls what is the probability of drawing two white balls from the jar?
13. Suppose six lines are drawn in the same plane. What is the largest possible number of intersection points of these lines? (Hint: what is the answer for two lines? three lines?)
14. How would you prove whether or not two lines are parallel? (How do you know that they don't intersect somewhere far off?)
15. What is the sum of the interior angles of an n-sided polygon?
16. What is the angle of one of the interior angles of a regular pentagon? a regular hexagon?
17. What is the sum of the exterior angles of an n-sided polygon?
18. Define a simple closed curve.
19. Draw a complicated simple closed curve, one with many, many curls and swirls. Now close your eyes and put your pencil down on the paper. Is it (your pencil) inside or outside of the curve? How do you know? (If you can tell by looking then you didn't make the curve complicated enough :))
20. Find two triangles, one acute and one obtuse, whose interior angle measures are each an integer multiple of . Give a drawing of each.
21. Are all polygons convex? If not, draw one which is not convex. Are all regular polygons convex? If not, draw one which is not convex.
22. What are skew lines?
23. How many planes are determined by the faces of a tetrahedron? Are any of the lines determined by the edges of a tetrahedron skew lines? Are any of them parallel lines?
24. For each statement decide whether it is true or false.
    1. Some right triangles are obtuse.
    2. It is possible that two angles interior to the same triangle may be supplementary
    3. Every square is an equilateral
    4. Every quadrilateral is a rhombus
    5. Any quadrilateral which has two pairs of congruent sides must be a rectangle.
    6. A triangle whose angles are all equal is an equilateral triangle
    7. A kite is a rectangle
    A connected planar network with 11 edges cuts the plane into 7 regions. How many vertices does the network have? Draw a connected planar network with 11 edges and 7 regions.
25. What is a traversable network?
26. Draw a connected network. Is the network traversable? How do you know?
27. If the network you drew above was traversable, are you allowed to start at any vertex? Or are there special starting points?

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